Councillor Tom Buchanan said he would be talking to the police about improving safety after a car left Gilmerton Station Road and ended up 30 metres away in a field.
Three people were thrown from the car and another had to be cut free.
Mr Buchanan, who represents Liberton/Gilmerton, said: "This just underlies the need for traffic-calming measures on this road.
It is known as a bit of a rat-run." Mr Buchanan said he would bring up the matter at the next meeting of the transport committee.
All five people in the car sustained serious injuries in the crash, which happened at about 11:30pm on Sunday.
All three female passengers were thrown out of the vehicle, while a male had to be cut free by fire crews.
Yesterday, Lothian and Borders Police said the female driver, who is 26, has been charged with dangerous driving and driving without a licence, while two passengers have been charged with unspecified offences under the road traffic act.
Source: Edinburgh Evening News
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